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# Full text of "Analytical Mechanics"

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```194                      ANALYTICAL MECHANICS
independent of the manner in which the change of configuration takes place, the forces acting upon the system are said to be conservative forces. Gravitational forces are examples of conservative forces. This is evident from the result of § 129; where it was shown that the work done against gravitational forces in taking a body from one point to another is independent of the path along which the body is carried.
160.   Dissipative Forces. — Forces which are not conservative are called dissipative or nonconservative forces.    All frie-tional and resisting forces are of this type.
161.   Potential Energy. — The potential energy of a system in any configuration equals the work done against the conservative forces which act upon the system, in bringing it from a standard configuration to the configuration in question.   For instance, if the unstretched state of an elastic string is taken to be its standard configuration, then the potential energy of the string at any stretched state equals the work done in producing the extension.    The potential energy of this book when on the table equals the work done in raising it from the floor to the table, provided the book is considered to be at the standard configuration when it is on the floor.
The selection of the standard configuration is quite arbitrary and is a matter of convenience only.
It is evident from the definition of potential energy that its value is zero at the standard configuration.
Comparing the definitions of potential energy and of conservative forces we see that the potential energy at any given configuration is independent of the manner in which the system is brought from the standard configuration. This is equivalent to stating that the potential energy of a system depends upon its configuration. But coordinates define the configuration of a system; therefore potential energy is a function of the coordinates.
If the sea level is taken as the standard configuration i.e., the position of zero potential energy, then the potential```